No, it's easier and less expensive to pull it once and so to speak "cache" them in the source code/clientside and perform the auto-complete without a server request. Otherwise it will be slower and more expensive as you hit the database or your LDAP directory for every key-event.
So every time I compose a new mail all my 500 (imagine 1000 or 5000 contacts!) are downloaded to the client... instead of just my girlfriends contact via AJAX whom I want to send a mail to. Not very efficient on slow connections!
Sounds like a case for HTML5 local storage . . .